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      <li class="navelem"><b>utils</b>      </li>
      <li class="navelem"><b>FemBases</b>      </li>
      <li class="navelem"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html">LagrangeP2</a>      </li>
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<a href="#pub-methods">Public Member Functions</a>  </div>
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<div class="title">utils::FemBases::LagrangeP2 Class Reference</div>  </div>
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<!-- doxytag: class="utils::FemBases::LagrangeP2" --><!-- doxytag: inherits="utils::FemBases::FemBasisBase" -->
<p>Inherits utils::FemBases::FemBasisBase.</p>

<p><a href="classutils_1_1FemBases_1_1LagrangeP2-members.html">List of all members.</a></p>
<table class="memberdecls">
<tr><td colspan="2"><h2><a name="pub-methods"></a>
Public Member Functions</h2></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#a17fbfeb603830e651f7596739459ba45">__init__</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#aa61c8d7ac412cb06175920f58e5518d8">derivatives</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><b>dof</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#a5b9cf434edd8071a8c35a8e8cb97e74e">get_grad_disp</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#ac51d628dcf4f7d5d746ad5242c9142b0">get_grad_grad</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><b>get_mass_mat</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><b>integrate</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#adc47860be69ef0d4dd395b1253deb93e">l1</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#a57100c2a57f2edc0583ded9f372ff978">l2</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#af64d5f5e7dd42e9b802305ce9c6eb3a3">l3</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#a7b781236f4fd0b13ee3129ac890774f8">second_der</a></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><b>shape_func_support</b></td></tr>
<tr><td class="memItemLeft" align="right" valign="top">def&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="classutils_1_1FemBases_1_1LagrangeP2.html#a0d03bbf9250b21e044f77e9597d9f6a1">values</a></td></tr>
</table>
<hr/><a name="details" id="details"></a><h2>Detailed Description</h2>
<div class="textblock"><div class="fragment"><pre class="fragment">compute the inner product
  ------- xi \in [-1, 1]
  </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00139">139</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>
</div><hr/><h2>Constructor &amp; Destructor Documentation</h2>
<a class="anchor" id="a17fbfeb603830e651f7596739459ba45"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::__init__" ref="a17fbfeb603830e651f7596739459ba45" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::__init__ </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">Instantiate an object to P2 type. </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00145">145</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<hr/><h2>Member Function Documentation</h2>
<a class="anchor" id="aa61c8d7ac412cb06175920f58e5518d8"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::derivatives" ref="aa61c8d7ac412cb06175920f58e5518d8" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::derivatives </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">evaluate at the derivatives of the shape fucntions. </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00213">213</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="a7ab82b62c5658a8f40c6b1d2507dd092"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::dof" ref="a7ab82b62c5658a8f40c6b1d2507dd092" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::FemBasisBase::dof </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em></td><td>)</td>
          <td><code> [inherited]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">degrees of freedom   </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00047">47</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="a5b9cf434edd8071a8c35a8e8cb97e74e"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::get_grad_disp" ref="a5b9cf434edd8071a8c35a8e8cb97e74e" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::get_grad_disp </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">compute matrix grad-displacment.  </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00191">191</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="ac51d628dcf4f7d5d746ad5242c9142b0"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::get_grad_grad" ref="ac51d628dcf4f7d5d746ad5242c9142b0" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::get_grad_grad </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em></td><td>)</td>
          <td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">compute grad-grad at reference element.  </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00181">181</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="ac0ac5340c77384495e2db6e365a55e56"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::get_mass_mat" ref="ac0ac5340c77384495e2db6e365a55e56" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::FemBasisBase::get_mass_mat </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em></td><td>)</td>
          <td><code> [inherited]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">get mass matrix.  </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00057">57</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="a244aaa1558bdbc1c0c623e50972ef646"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::integrate" ref="a244aaa1558bdbc1c0c623e50972ef646" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::FemBasisBase::integrate </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>i</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>j</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td><code> [inherited]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">integrate two shape functions in reference interval.</pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00062">62</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
</div>
<a class="anchor" id="adc47860be69ef0d4dd395b1253deb93e"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::l1" ref="adc47860be69ef0d4dd395b1253deb93e" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::l1 </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">L_1(pointsi) = -0.5*pointsi*(1.0-pointsi) </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00151">151</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

<p>Referenced by <a class="el" href="FemBases_8py_source.html#l00203">values()</a>.</p>

</div>
</div>
<a class="anchor" id="a57100c2a57f2edc0583ded9f372ff978"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::l2" ref="a57100c2a57f2edc0583ded9f372ff978" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::l2 </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">N_2(pointsi) = 1.0-pointsi**2 </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00158">158</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

<p>Referenced by <a class="el" href="FemBases_8py_source.html#l00203">values()</a>.</p>

</div>
</div>
<a class="anchor" id="af64d5f5e7dd42e9b802305ce9c6eb3a3"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::l3" ref="af64d5f5e7dd42e9b802305ce9c6eb3a3" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::l3 </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">N_3(pointsi) =  0.5*pointsi*(1+pointsi) </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00165">165</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

<p>References <a class="el" href="FemBases_8py_source.html#l00033">utils::FemBases::FemBasisBase::m_mass</a>, <a class="el" href="FemBases_8py_source.html#l00089">utils::FemBases::LagrangeP1::m_mass</a>, and <a class="el" href="FemBases_8py_source.html#l00171">m_mass</a>.</p>

<p>Referenced by <a class="el" href="FemBases_8py_source.html#l00203">values()</a>.</p>

</div>
</div>
<a class="anchor" id="a7b781236f4fd0b13ee3129ac890774f8"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::second_der" ref="a7b781236f4fd0b13ee3129ac890774f8" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::second_der </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>cls</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">second derivative of shape functions. </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00220">220</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
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<a class="anchor" id="a64d8e5a208d8ac7f87c2fd397cb53c18"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::shape_func_support" ref="a64d8e5a208d8ac7f87c2fd397cb53c18" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::FemBasisBase::shape_func_support </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em></td><td>)</td>
          <td><code> [inherited]</code></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">return extrems defineing domain for shape functions. </pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00052">52</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

</div>
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<a class="anchor" id="a0d03bbf9250b21e044f77e9597d9f6a1"></a><!-- doxytag: member="utils::FemBases::LagrangeP2::values" ref="a0d03bbf9250b21e044f77e9597d9f6a1" args="" -->
<div class="memitem">
<div class="memproto">
      <table class="memname">
        <tr>
          <td class="memname">def utils::FemBases::LagrangeP2::values </td>
          <td>(</td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>self</em>, </td>
        </tr>
        <tr>
          <td class="paramkey"></td>
          <td></td>
          <td class="paramtype">&#160;</td>
          <td class="paramname"><em>points</em>&#160;</td>
        </tr>
        <tr>
          <td></td>
          <td>)</td>
          <td></td><td></td>
        </tr>
      </table>
</div>
<div class="memdoc">
<div class="fragment"><pre class="fragment">evaluate shape function at points.</pre></div> 
<p>Definition at line <a class="el" href="FemBases_8py_source.html#l00203">203</a> of file <a class="el" href="FemBases_8py_source.html">FemBases.py</a>.</p>

<p>References <a class="el" href="FemBases_8py_source.html#l00079">utils::FemBases::LagrangeP1::l1()</a>, <a class="el" href="FemBases_8py_source.html#l00151">l1()</a>, <a class="el" href="FemBases_8py_source.html#l00084">utils::FemBases::LagrangeP1::l2()</a>, <a class="el" href="FemBases_8py_source.html#l00158">l2()</a>, and <a class="el" href="FemBases_8py_source.html#l00165">l3()</a>.</p>

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